Finding the time of arrival between two balls in air using kinematics

In summary, the problem asks for the time when two balls, one thrown upward from the ground and one dropped from a building, will reach the same height. Using equations of kinematics, the initial velocities and accelerations of the balls are taken into account to find the time difference between them. However, this approach only finds the time when they have the same velocity, not the same height. Instead, setting up equations for the height of each ball at a given time and equating them will give the correct answer.
  • #1
garcia1
27
0

Homework Statement


A ball is thrown upward from the ground with
an initial speed of 51 m/s; at the same instant,
a ball is dropped from a building 38 m high.
After how long will the balls be at the
same height? The acceleration of gravity is
9.8 m/s2 .
Answer in units of s.


Homework Equations



Equations of Kinematics


The Attempt at a Solution


I thought that by finding the time difference between the two that it would give me the answer.

Setting up the equation as DeltaT = T1 - T2, I found the times for each object using equation Vf = Vi + at for the object with a velocity of 51m/s, and the equation x = Vo*t + 1/2at^2 for the object 38 meters above the ground. Finding the time for these two, I plugged them into my DeltaT equation, with the biggest value as T1.

I got the answer 2.42s, but this was wrong.
 
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  • #2
hi garcia1! :wink:
garcia1 said:
Setting up the equation as DeltaT = T1 - T2, I found the times for each object using equation Vf = Vi + at for the object with a velocity of 51m/s …

i don't understand … how do you know Vf ? :confused:

why not use the same equation for both balls (with different x0 and v0 of course)? :smile:
 
  • #3
What I thought you meant by this was that I should set both equations equal to a common variable, and then solve for T accordingly. I tried this with the variable Vf, solving for both in this way:

Eq 1: Vf = Vo +at
Eq 2: Vf^2 = Vo^2 + 2ax -> Vf = rad(Vo^2 + 2ax)

Then setting them equal to each other: Vo + at = rad(Vo^2 + 2ax) - Vo
a

I solved for t, and got the answer T = 2.42s, but this was wrong. Any thoughts on where I messed up?
 
  • #4
The second equation is over a. Sorry, computing error.
 
  • #5
You're trying to find when both balls will be at the same height. So wouldn't it be a good idea to write an equation for each ball which gives the height at a given time and then equate them?
 
  • #6
hi garcia1! :smile:

(just got up :zzz: …)
garcia1 said:
What I thought you meant by this was that I should set both equations equal to a common variable, and then solve for T accordingly. I tried this with the variable Vf …

but that will only give you the time T at which they both have the same velocity, won't it? :wink:
 

Related to Finding the time of arrival between two balls in air using kinematics

1. How do you calculate the time of arrival between two balls in air using kinematics?

To calculate the time of arrival between two balls in air using kinematics, you will need to know the initial velocity, acceleration, and displacement of the two balls. Then, you can use the time formula t = (vf - vi) / a to determine the time of arrival, where vf is the final velocity, vi is the initial velocity, and a is the acceleration.

2. What is the difference between time of flight and time of arrival in kinematics?

In kinematics, the time of flight refers to the total time that a projectile or object is in the air, while the time of arrival specifically refers to the time it takes for an object to travel from its initial position to its final position. The time of arrival is typically calculated by using the time formula t = (vf - vi) / a, where vf is the final velocity, vi is the initial velocity, and a is the acceleration.

3. How does air resistance affect the time of arrival between two balls in air?

Air resistance can have a significant impact on the time of arrival between two balls in air. It can cause the balls to slow down and change their trajectory, leading to a longer time of arrival. Additionally, air resistance can also vary depending on the density and shape of the objects, which can further affect the time of arrival.

4. Can you use kinematics to calculate the time of arrival between two balls in air without knowing their initial velocity?

No, you cannot calculate the time of arrival between two balls in air using kinematics without knowing their initial velocity. This is because the time formula t = (vf - vi) / a requires both the final velocity and initial velocity to determine the time of arrival. Without knowing the initial velocity, it is not possible to accurately calculate the time of arrival.

5. Are there any limitations to using kinematics to find the time of arrival between two balls in air?

Yes, there are limitations to using kinematics to find the time of arrival between two balls in air. Kinematics assumes that there is no air resistance or other external forces acting on the objects, which may not be true in real-life scenarios. Additionally, kinematics does not take into account the shape and density of the objects, which can also affect the time of arrival. Therefore, the calculated time of arrival using kinematics may not be entirely accurate in all situations.

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